Lisa just got a new math workbook. A workbook contains exercise problems, grouped into chapters. Lisa believes a problem to be special if its index (within a chapter) is the same as the page number where it’s located. The format of Lisa’s book is as follows:

• There are n chapters in Lisa’s workbook, numbered from 1 to n.
• The chapter has arr[i] problems, numbered from 1 to arr[i].
• Each page can hold up to k problems. Only a chapter’s last page of exercises may contain fewer than k problems.
• Each new chapter starts on a new page, so a page will never contain problems from more than one chapter.
• The page number indexing starts at 1.

Calvin is driving his favorite vehicle on the 101 freeway. He notices that the check engine light of his vehicle is on, and he wants to service it immediately to avoid any risks. Luckily, a service lane runs parallel to the highway. The service lane varies in width along its length.

You will be given an array of widths at points along the road (indices), then a list of the indices of entry and exit points. Considering each entry and exit point pair, calculate the maximum size vehicle that can travel that segment of the service lane safely.

For example, there are n = 4 measurements yielding width = [2, 3, 2, 1]. If our entry index, i = 1 and our exit, j = 2, there are two segment widths of 2 and 3 respectively. The widest vehicle that can fit through both is 2. If i = 2 and j = 4, our widths are [3, 2, 1] which limits vehicle width to 1.

Little Bobby loves chocolate. He frequently goes to his favorite 5 & 10 store, Penny Auntie, to buy them. They are having a promotion at Penny Auntie. If Bobby saves enough wrappers, he can turn them in for a free chocolate.

For example, Bobby has n = 15 to spend on bars of chocolate that cost c = 3 each. He can turn in m = 2 wrappers to receive another bar. Initially, he buys 5 bars and has 5 wrappers after eating them. He turns in 4 of them, leaving him with 1, for 2 more bars. After eating those two, he has 3 wrappers, turns in 2 leaving him with 1 wrapper and his new bar. Once he eats that one, he has 2 wrappers and turns them in for another bar. After eating that one, he only has 1 wrapper, and his feast ends. Overall, he has eaten 5 + 2 + 1 + 2 = 9 bars.

You wish to buy video games from the famous online video game store Mist.

Usually, all games are sold at the same price, p dollars. However, they are planning to have the seasonal Halloween Sale next month in which you can buy games at a cheaper price. Specifically, the first game you buy during the sale will be sold at p dollars, but every subsequent game you buy will be sold at exactly d dollars less than the cost of the previous one you bought. This will continue until the cost becomes less than or equal to m dollars, after which every game you buy will cost m dollars each.

For example, if p = 20, d = 3 and m = 6, then the following are the costs of the first 11 games you buy, in order:

20, 17, 14, 11, 8, 6, 6, 6, 6, 6, 6

You have s dollars in your Mist wallet. How many games can you buy during the Halloween Sale?

We define the distance between two array values as the number of indices between the two values. Given a, find the minimum distance between any pair of equal elements in the array. If no such value exists, print -1.

For example, if a = [3, 2, 1, 2, 3], there are two matching pairs of values: 3 and 2. The indices of the 3‘s are i = 0 and j = 4, so their distance is d[i, j] = |j - i| = 4. The indices of the 2‘s are i = 1 and j = 3, so their distance is d[i, j] = |j - i| = 2.

Given a sequence of integers a, a triplet (a[i], a[j], a[k]) is beautiful if:

• i < j < k
• a[j] - a[i] = a[k] - a[j] = d

Given an increasing sequenc of integers and the value of d, count the number of beautiful triplets in the sequence.

For example, the sequence arr = [2, 2, 3, 4, 5] and d = 1. There are three beautiful triplets, by index: [i, j, k] = [0, 2, 3], [1, 2, 3], [2, 3, 4]. To test the first triplet, arr[j] - arr[i] = 3 - 2 = 1 and arr[k] = arr[j] = 4 - 3 = 1.

A modified Kaprekar number is a positive whole number with a special property. If you square it, then split the number into two integers and sum those integers, you have the same value you started with.

Consider a positive whole number n with d digits. We square n to arrive at a number that is either 2 x d digits long or (2 x d) - 1 digits long. Split the string representation of the square into two parts, l and r. The right hand part, r must be d digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get n.

For example, if n = 5, d = 1 then . We split that into two strings and convert them back to integers 2 and 5. We test , so this is not a modified Kaprekar number. If n = 9, still d = 1, and . This gives us 1 + 8 = 9, the original n.

Note: r may have leading zeros.

An English text needs to be encrypted using the following encryption scheme.
First, the spaces are removed from the text. Let L be the length of this text.
Then, characters are written into a grid, whose rows and columns have the following constraints:

For example, the sentence
s = if man was meant to stay on the ground god would have given us roots, after removing spaces is 54 characters long. is between 7 and 8, so it is written in the form of a grid with 7 rows and 8 columns.

Taum is planning to celebrate the birthday of his friend, Diksha. There are two types of gifts that Diksha wants from Taum: one is black and the other is white. To make her happy, Taum has to buy b black gifts and w white gifts.

• The cost of each black gift is bc units.
• The cost of every white gift is wc units.
• The cost of converting each black gift into white gift or vice versa is z units.

Help Taum by deducing the minimum amount he needs to spend on Diksha’s gifts.

For example, if Taum wants to buy b = 3 black gifts and w = 5 white gifts at a cost of bc = 3, wc = 4 and conversion cost z = 1, we see that he can buy a black gift for 3 and convert it to a white gift for 1, making the total cost of each white gift 4. That matches the cost of a white gift, so he can do that or just buy black gifts and white gifts. Either way, the overall cost is 3 * 3 + 5 * 4 = 29.

You are given a number of sticks of varying lengths. You will iteratively cut the sticks into smaller sticks, discarding the shortest pieces until there are none left. At each iteration you will determine the length of the shortest stick remaining, cut that length from each of the longer sticks and then discard all the pieces of that shortest length. When all the remaining sticks are the same length, they cannot be shortened so discard them.

Given the lengths of n sticks, print the number of sticks that are left before each iteration until there are none left.

For example, there are n = 3 sticks of lengths arr = [1, 2, 3]. The shortest stick length is 1, so we cut that length from the longer two and discard the pieces of length 1. Now our lengths are arr = [1, 2]. Again, the shortest stick is of length 1, so we cut that amount from the longer stick and discard those pieces. There is only one stick left, arr = [1], so we discard that stick. Our lengths are answer = [3, 2, 1].